The maximum error in measurement of mass and density of a cube are 2% and 1%, respectively. The maximum percentage error in measurement of volume will be

Introduction

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Solution:

The relationship between mass (m), density (ρ), and volume (V) is given by:

ρ = m/V

Rearranging for volume, we get:

V = m/ρ

When quantities are multiplied or divided, their maximum percentage errors add up. The formula for the maximum percentage error in V is:

(ΔV/V) * 100% = (Δm/m) * 100% + (Δρ/ρ) * 100%

Given:

Maximum percentage error in mass (Δm/m * 100%) = 2%

Maximum percentage error in density (Δρ/ρ * 100%) = 1%

Substituting these values into the formula:

(ΔV/V) * 100% = 2% + 1%

(ΔV/V) * 100% = 3%

Thus, the maximum percentage error in the measurement of volume will be 3%.